On the quantitative quasi-isometry problem: transport of Poincaré inequalities and different types of quasi-isometric distortion growthReport as inadecuate




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1 LM-Orsay - Laboratoire de Mathématiques d-Orsay

Abstract : We consider a quantitative form of the quasi-isometry problem. We discuss several arguments which lead us to different results and bounds of quasi-isometric distortion: comparison of volumes, connectivity etc. Then we study the transport of Poincaré constants by quasi-isometries and we give sharp lower and upper bounds for the homotopy distortion growth for an interesting class of hyperbolic metric spaces.

Mots-clés : Quasi-isometries hyperbolic spaces Poincaré constants quantitative quasi-isometry problem





Author: Vladimir Shchur -

Source: https://hal.archives-ouvertes.fr/



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